Comments on gauge theories without anomalies

Anomaly-free gauge theories corresponding to "safe" simple Lie groups classified by Georgi and Glashow are further analyzed under the requirement that they contain no fractionally or doubly charged particles. It is found that orthogonal groups SO(N) can satisfy this restriction when the leptons transform as an irreducible "fundamental" representation of SO(N). For the symplectic groups Sp(2N), this is true if the lepton representation is the adjoint representation or the representation ρ2 defined below. If the leptons are to transform as the lowest-dimensional representation, it is necessary to consider product groups of the form Sp(2N)â-U(1). The exceptional group G2 is ruled out.